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Jacobi-Anger Expansion

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e^(izcostheta)=sum_(n=-infty)^inftyi^nJ_n(z)e^(intheta),

where J_n(z) is a Bessel function of the first kind. The identity can also be written

e^(izcostheta)=J_0(z)+2sum_(n=1)^inftyi^nJ_n(z)cos(ntheta).

This expansion represents an expansion of plane waves into a series of cylindrical waves.

See also

Bessel Function of the First Kind

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Cite this as:

Weisstein, Eric W. "Jacobi-Anger Expansion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Jacobi-AngerExpansion.html

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